Expression of type Forall ¶

from the theory of proveit.physics.quantum.QPE ¶

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprRange, U, Variable, VertExprArray, s, t
from proveit.linear_algebra import Unitary
from proveit.logic import Forall
from proveit.numbers import Add, Exp, Interval, NaturalPos, one, two
from proveit.physics.quantum.QPE import QPE1, QPE1_U_t_circuit
from proveit.physics.quantum.circuits import Gate, MultiQubitElem, Qcircuit, QcircuitEquiv

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(t, s)
sub_expr3 = MultiQubitElem(element = Gate(operation = QPE1(U, t), part = sub_expr1), targets = Interval(one, sub_expr2))
expr = Forall(instance_param_or_params = [s, t], instance_expr = Forall(instance_param_or_params = [U], instance_expr = QcircuitEquiv(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, sub_expr3, one, t), ExprRange(sub_expr1, sub_expr3, Add(t, one), sub_expr2)])), QPE1_U_t_circuit), domain = Unitary(Exp(two, s))), domain = NaturalPos)

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{s, t \in \mathbb{N}^+}~\left[\forall_{U \in \textrm{U}\left(2^{s}\right)}~\left(\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \multigate{1}{\textrm{QPE}_1\left(U, t\right)} & { /^{t} } \qw \\
& \ghost{\textrm{QPE}_1\left(U, t\right)} & { /^{s} } \qw
} \end{array}\right) \cong \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \control{} \qw \qwx[1] & \qw & \gate{\cdots} \qwx[1] & \qw & \qw \\
& \qw \qwx[1] & \control{} \qw \qwx[1] & \gate{\cdots} \qwx[1] & \qw & \qw \\
& \gate{\vdots} \qwx[1] & \gate{\vdots} \qwx[1] & \gate{\ddots} \qwx[1] & \gate{\vdots} & \qw \\
& \qw \qwx[1] & \qw \qwx[1] & \gate{\cdots} \qwx[1] & \control{} \qw \qwx[1] & \qw \\
& \gate{U^{2^{t - 1}}} & \gate{U^{2^{t - 2}}} & \gate{\cdots} & \gate{U^{2^{0}}} & { /^{s} } \qw
} \end{array}\right)\right)\right]

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

	core type	sub-expressions
0	Operation	operator: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	99, 107
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 11
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11
9	Literal
10	ExprTuple	12, 13
11	Lambda	parameter: 97 body: 15
12	Operation	operator: 23 operands: 16
13	Operation	operator: 23 operands: 17
14	ExprTuple	97
15	Conditional	value: 18 condition: 19
16	ExprTuple	99, 20
17	ExprTuple	107, 20
18	Operation	operator: 21 operands: 22
19	Operation	operator: 23 operands: 24
20	Literal
21	Literal
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	97, 27
25	Operation	operator: 29 operand: 33
26	Operation	operator: 29 operands: 30
27	Operation	operator: 31 operand: 35
28	ExprTuple	33
29	Literal
30	ExprTuple	34
31	Literal
32	ExprTuple	35
33	ExprTuple	36, 37
34	ExprRange	lambda_map: 38 start_index: 39 end_index: 40
35	Operation	operator: 101 operands: 41
36	ExprRange	lambda_map: 42 start_index: 108 end_index: 107
37	ExprRange	lambda_map: 42 start_index: 100 end_index: 85
38	Lambda	parameter: 111 body: 43
39	Operation	operator: 103 operands: 44
40	Literal
41	ExprTuple	105, 99
42	Lambda	parameter: 90 body: 45
43	ExprTuple	46, 47
44	ExprTuple	48, 108
45	Operation	operator: 77 operands: 49
46	ExprRange	lambda_map: 50 start_index: 108 end_index: 107
47	ExprRange	lambda_map: 51 start_index: 108 end_index: 99
48	Operation	operator: 109 operand: 107
49	NamedExprs	element: 53 targets: 54
50	Lambda	parameter: 90 body: 55
51	Lambda	parameter: 90 body: 57
52	ExprTuple	107
53	Operation	operator: 80 operands: 58
54	Operation	operator: 75 operands: 59
55	Operation	operator: 60 operands: 61
56	ExprTuple	90
57	Operation	operator: 77 operands: 62
58	NamedExprs	operation: 63 part: 90
59	ExprTuple	108, 85
60	Literal
61	ExprTuple	64, 65
62	NamedExprs	element: 66 targets: 67
63	Operation	operator: 68 operands: 69
64	Conditional	value: 70 condition: 71
65	Conditional	value: 72 condition: 73
66	Operation	operator: 80 operands: 74
67	Operation	operator: 75 operands: 76
68	Literal
69	ExprTuple	97, 107
70	Operation	operator: 77 operands: 78
71	Operation	operator: 79 operands: 83
72	Operation	operator: 80 operands: 81
73	Operation	operator: 82 operands: 83
74	NamedExprs	operation: 84 part: 90
75	Literal
76	ExprTuple	100, 85
77	Literal
78	NamedExprs	element: 86 targets: 87
79	Literal
80	Literal
81	NamedExprs	operation: 88
82	Literal
83	ExprTuple	89, 90
84	Operation	operator: 91 operands: 92
85	Operation	operator: 103 operands: 93
86	Literal
87	Operation	operator: 94 operand: 100
88	Literal
89	Operation	operator: 103 operands: 96
90	Variable
91	Literal
92	ExprTuple	97, 98
93	ExprTuple	107, 99
94	Literal
95	ExprTuple	100
96	ExprTuple	111, 107
97	Variable
98	Operation	operator: 101 operands: 102
99	Variable
100	Operation	operator: 103 operands: 104
101	Literal
102	ExprTuple	105, 106
103	Literal
104	ExprTuple	107, 108
105	Literal
106	Operation	operator: 109 operand: 111
107	Variable
108	Literal
109	Literal
110	ExprTuple	111
111	Variable

Expression of type Forall¶

from the theory of proveit.physics.quantum.QPE¶

Expression of type Forall ¶

from the theory of proveit.physics.quantum.QPE ¶